Unexploited Gains From International Diversification:
Patterns Of Portfolio Holdings Around The World
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Citation
Didier, Tatiana, Roberto Rigobon, and Sergio L. Schmukler.
“Unexploited Gains From International Diversification: Patterns
Of Portfolio Holdings Around The World.” Review of Economics
and Statistics 95, no. 5 (December 2013): 1562–1583. © 2013
The President and Fellows of Harvard College and the
Massachusetts Institute of Technology
As Published
http://dx.doi.org/10.1162/REST_a_00351
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MIT Press
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UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION:
PATTERNS OF PORTFOLIO HOLDINGS AROUND THE WORLD
Tatiana Didier, Roberto Rigobon, and Sergio L. Schmukler*
Abstract—Using unique data on mutual fund portfolios with different
investment scopes, we study the extent of international diversification.
Mutual funds invest in a surprisingly limited number of stocks—about
100. The number of holdings from a given region declines as the investment scope broadens. Moreover, unexploited gains exist from international diversification. Funds that invest globally could achieve better riskadjusted returns by adding stocks held by more specialized funds within
the same family. These findings are not driven by different sectoral allocations, lack of information or instruments, transaction costs, or different
tail risks. Instead, organizational factors might play an important role.
I.
Introduction
S
INCE the 1990s, the growth in financial globalization
has been remarkable. Institutional investors have been
significant contributors to this growth by purchasing foreign
assets. Given standard economic theory, one might expect
to see significant international diversification accompanying
the globalization process. Yet, to date, little evidence exists
on how investors allocate their global portfolios and what
determines their decisions.
In this paper, we aim to fill this gap in the literature by
constructing and analyzing a unique micro data set of assetlevel portfolios for a group of relevant global institutional
investors: U.S. equity mutual funds with an international
investment scope. We document important stylized facts
regarding their global asset allocations and analyze the drivers of their portfolio decisions.
The data on mutual funds offer significant advantages for
the empirical analysis. First, mutual funds, unlike other
Received for publication March 19, 2011. Revision accepted for publication August 17, 2012.
* Didier: World Bank; Rigobon: MIT and NBER; Schmukler: World Bank.
For very helpful comments, thank Andres Almazan, Deniz Anzinger,
Fernando Broner, Ricardo Caballero, Charlie Calomiris, V.V. Chari, Asli
Demirguc-Kunt, Bob Gibbons, Julian di Giovanni, Alejandro Drexler,
Pierre-Olivier Gourrinchas, Gordon Hanson (the Editor), Heiko Jacobs,
Graciela Kaminsky, Mark Kritzman, Michael Klein, Tarun Ramadorai,
Rafael Repullo, Dani Rodrik, Rafael Chaves Santos, Luis Servén, Steven
Snider, Frank Warnock, two anonymous referees, and participants at the
presentations held at the AEA Annual Meetings (Chicago), the Dutch
National Bank, the European Central Bank, Harvard University, the Helsinki Finance Summit on Investor Behavior, the IMF Ninth Jacques Polak
Annual Research Conference, the LACEA Annual Meetings (Buenos Aires
and Mexico City), MIT, the NBER Summer Institute, the NIPFP-DEA
Workshop on Capital Flows (New Delhi), the XII Workshop in International Economics and Finance (Rio de Janeiro), and the World Bank. This
paper received the 2011 Finance and Private Sector Development Academy Award from the World Bank. We are grateful to Tiago Caruso, Francisco Ceballos, Juan Carlos Gozzi, Jennifer Kim, Ricardo Leal, Julian
Kozlowski, Lucas Nuñez, Paula Pedro, Mercedes Politi, Virginia Poggio,
Juliana Portella, Mira Olson, and Matias Vieyra, who provided excellent
research assistance at different stages of the project; and Judith Goff and
Jonathan Moore, who helped with the editing. The World Bank provided
generous financial support through its Development Economics Department and Knowledge for Change Program. The views expressed here do
not necessarily represent those of the World Bank.
A supplemental appendix is available online at http://www.mitpress
journals.org/doi/suppl/10.1162/REST_a_00351.
types of investors, face regular reporting requirements.
Thus, a data set based on asset-level portfolios can be constructed and traced for a relatively long time. Second, the
structure of mutual fund families allows us to make withinfamily comparisons between the behavior of specialized
funds (which can invest only in certain countries or regions)
and global funds (which can invest anywhere in the world
and thus have access to a larger set of firms from more
countries). For mutual fund managers, knowing that a fund
holds certain stocks is an indication that the transaction
costs to hold them are not exceedingly large and that those
stocks are indeed desirable (at least to other fund managers
within the same family). Moreover, information about those
stocks has already been collected at the firm level and, in
principle, might be available to all managers in that family.
Therefore, the relevance of information sharing and transaction costs discussed in the literature can be analyzed by
comparing portfolios across funds within the same mutual
fund family and across families. In addition, the returns of
specialized funds can be compared to those of global funds.
These returns are net of the transaction costs that funds pay
when investing in different types of stocks.
We collect portfolio holding and return data for the universe of actively managed open-end U.S. equity mutual
funds established to purchase assets around the world. The
data on holdings contain asset-level annual portfolios
between 1991 and 2005. We work with 499 fund families
and 1,904 funds. The total number of fund-year observations is 8,420 and the total number of asset-level holdings
for all funds in all years is 1,359,750. We compute daily
returns at the fund level using a longer time series (between
September 1989 and June 2006) for 36 fund families that
have a variety of mutual funds for which useful comparisons can be made. We work with a total of 722,885 daily
observations that comprise the returns from all of the funds
in these families.
Four initial stylized facts about the international investments of mutual funds emerge from our analysis. First, global funds have grown much more than specialized funds.
Second, both specialized and global mutual funds hold a
similar number of stocks (the average number of stocks is
150, and the median 95). In fact, the number of asset holdings in the mutual fund portfolios does not tend to be higher
for global funds compared to specialized funds within the
same mutual fund family, even though the pool of investable assets is significantly larger for global funds. Third,
within each region of exposure, global funds hold fewer
assets from fewer countries when compared to specialized
funds within the same mutual fund family. Fourth, this
reduction in the number of stocks is not matched by a
reduction in the number of economic sectors they invest in.
The Review of Economics and Statistics, December 2013, 95(5): 1562–1583
Ó 2013 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
In fact, the sectoral allocation is similar across global and
specialized funds. This investment pattern of global funds
is relevant because these funds are investing an increasing
amount of resources in stocks from a limited set of companies and countries.
The natural question then is, what might explain this
restrictive investment practice? First, instrument availability or transaction costs do not appear to be the driving
forces. The cross-fund comparison is especially revealing in
this case: the fact that one particular fund holds a certain
stock is an indication that no clear investment restrictions
related to that company exist and that the transaction costs
are small enough for that fund to hold that stock. Our point
of comparison is the funds within the same family that differ only in their investment scope. For example, global
funds, which hold particularly few stocks, could expand
their holdings by investing in the stocks that specialized
funds within the same firm hold.
Second, by itself, the lack of information at the family
level does not seem to explain the apparent lack of international diversification by mutual funds. The problem seems
to reside on how information is used across funds within a
family. If global and specialized funds within families share
information and make similar decisions, one can expect to
observe similar portfolios among them. However, we find
that the portfolios of global and specialized funds within
families are different and that global funds do not seem to
follow specialized funds in their portfolio allocations. We
also find that the portfolios become more similar when global and specialized funds are managed by some of the same
managers, and the similarity increases with the number of
common managers. This evidence does not appear to be
consistent with managers using, to a large extent, information already gathered or processed by other managers
within the same mutual fund family; instead, the evidence
seems consistent with competition between managers.
Third, mutual fund family effects appear to be a strong
driving factor behind the portfolio choices of individual
funds. A large dispersion exists in the number of stocks
held around the world by mutual funds across different
families. Family effects explain almost 50% of the crosssectional and time series variation in the number of stock
holdings and the loadings on the top ten holdings. These
effects vastly exceed the explanatory power of the commonly used measures that capture the abilities of funds and
managers to gather and process information and select portfolios.
The fact that global funds do not tend to hold more stocks
than specialized funds does not necessarily imply a diversification loss for the investors who own the global funds. If
asset returns within and across countries are perfectly correlated, global funds will be able to obtain the same degree of
diversification benefits as specialized funds by holding
fewer stocks, possibly in fewer countries. Thus, return correlations could account for the patterns observed in the
data.
1563
Our analysis suggests that unexploited diversification
gains exist and that global funds could benefit from investing in more stocks. To explore this possibility, we first use
a mean-variance optimization framework to estimate the
performance of simulated global funds, each constructed as
a portfolio of specialized funds within a mutual fund
family. We then compare the performance of these simulated global funds to that of the corresponding actual global
funds within the same family. This exercise is very restrictive because the simulated global funds cannot hold any
stock available to any specialized fund; rather, they must
invest in a portfolio already held by another fund within
their fund family. This restriction guarantees that the stocks
are available for investment and are attractive to at least
one other manager in the same family and that information
about the stocks has already been collected and analyzed by
someone working within the same organization as the global fund manager. Our results suggest that global funds
could obtain better risk-adjusted returns (between 2.6% and
5.5% per year) if they invest in portfolios that include holdings similar to those of specialized funds within the same
mutual fund family.
We also explore whether there is an insurance premium
in the returns of global funds. Because global funds can
secure gains by moving away from troubled countries,
investors might be willing to pay for this benefit and accept
lower expected returns. However, global funds do not seem
to better shield investors from tail risk. The skewness and
the kurtosis of the global fund returns are similar to those of
the simulated global funds. Moreover, conditional on large
negative returns from either the specialized funds or the
MSCI Emerging Market Index, the returns from the simulated global funds are broadly similar to those of the global
funds. In sum, the lack of diversification in global funds
does not seem to be explained by a better performance during turbulent times.
The analysis in this paper of microlevel international
portfolios allows us to contribute to several strands of the
academic literature. Our focus on mutual funds with a global reach enables us to shed light on the forces behind the
growing but still limited international diversification.
Importantly, by studying mutual fund portfolios within and
across fund families (companies), we depart from the standard approach in the international diversification literature
that focuses mostly on aggregate measures to characterize
investment patterns across countries.1 Moreover, our analysis on how the organization of financial intermediaries can
affect investment decisions complements the industrial
organization literature. This literature suggests that management practices and idiosyncratic firm effects can explain
1
Although researchers have begun to exploit asset-level data, as in
Strong and Xu (2003), Edison and Warnock (2004), Eun, Huang, and Lai
(2008), and Hau and Rey (2008), the evidence remains scarce. For some
of the aggregate evidence, see, for example, Tesar and Werner (1995),
Kraay et al. (2005), Portes and Rey (2005), and Lane and Milesi-Ferretti
(2008).
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THE REVIEW OF ECONOMICS AND STATISTICS
FIGURE 1.—STYLIZED STRUCTURE OF THE U.S. MUTUAL FUND FAMILIES
Global
Funds
World Funds
Foreign Funds
U.S. Funds
Specialized
Funds
Emerging Market Funds
Regional Fund
Asia
Country Fund
China
Country Fund
Japan
Regional Fund
Europe
Country Fund
S. Korea
Regional Fund
Emerging Asia
Regional Fund
Eastern Europe
Regional Fund
Latin America
+ …
Regional Fund
Middle East
+ …
+ …
This figure characterizes the organizational structure of the U.S. mutual fund families that invest in foreign assets. The figure also shows our classification criteria for global and specialized funds. Global funds
comprise both world and foreign funds. Specialized funds comprise emerging market, regional, and country funds. The names used in this figure to characterize specialized funds are just examples.
corporate behavior, diversification, and performance.2 Our
paper is also related to the finance literature that argues that
incentive misalignments might lead managers to hold suboptimal portfolios for investors.3 Furthermore, by analyzing
mutual funds with different investment scopes across countries, we contribute to the literature on the investment patterns of institutional investors.4
The rest of the paper is organized as follows. Section II
describes the data. Section III studies how mutual funds
allocate their portfolios internationally. Section IV analyzes
the factors behind the degree of diversification. Section V
studies whether there are potential costs to the diversification strategies of global funds. Section VI concludes.
II.
Data
We use two types of data: holdings and returns from
equity funds in the large and sophisticated U.S. mutual fund
industry, established to purchase assets around the world.
2
A number of papers in this literature emphasize these effects in different contexts. See Nelson (1991), Bartelsman and Doms (2000), Black and
Lynch (2001), Bertrand and Schoar (2003), Bloom and Van Reenen
(2007), and Gibbons and Henderson (2012), among many others.
3
See Shleifer and Vishny (1990), Brown, Harlow, and Starks (1996),
Chevalier and Ellison (1997, 1999), Dow and Gorton (1997), Bolton,
Freixas, and Shapiro (2004), and Stein (2005), among others.
4
A strand of this literature studies the investment patterns of institutional investors in foreign markets. See, for example, Kang and Stulz
(1997), Dahlquist and Robertsson (2001), Grinblatt and Keloharju (2001),
Kim and Wei (2002), Kaminsky, Lyons, and Schmukler (2004), Chan,
Covrig, and Ng (2005), Gelos and Wei (2005), Broner, Gelos, and Reinhart (2006), Jotikasthira, Lundblad, and Ramadorai (2012), and Raddatz
and Schmukler (2012).
The U.S. mutual fund industry is organized by splitting
funds according to their investment scope (figure 1). In particular, five classifications exist: world funds, foreign funds,
emerging market funds, regional funds, and country funds.
World funds invest all over the world, including the United
States. Foreign funds invest around the world, excluding the
United States. Emerging market funds invest only in emerging market assets. Regional funds invest only in specific
regions and are typically called Asia (and Pacific) funds,
Europe funds, Latin America (and Caribbean) funds, and so
forth. Country funds are similar in that they invest only in
specific countries. For ease of exposition, we group the funds
into two categories: global funds and specialized funds. Global funds encompass world funds and foreign funds. All
other fund types are called specialized funds, and each of
these funds can invest only in a subset of the assets available
to global funds. Global funds are always able to invest in the
stocks held by specialized funds, but not vice versa.
The data on the mutual fund portfolio holdings come
from Morningstar. Using the last reported portfolio for each
fund in any given year, we compile end-of-year detailed
information on the portfolio holdings between 1991 and
2005. We gather information on the stock names, the
amount invested in each stock by each fund, the sectoral
classification, and the country of origin for the stocks
(regardless of where they trade).5 One difficulty in constructing this database is that mutual funds report their
5
The funds considered in the analysis invest almost exclusively in publicly listed companies. Although mutual funds are allowed to invest at
most 15% of their assets in illiquid or thinly traded securities (including
private companies), investment in private firms appears to be, if any, very
small (typically less than 0.3% of the portfolios).
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
asset allocations separately over time. Therefore, each
security needs to be identified at each point in time and then
matched over time with the different fund portfolios.
We collect data on 8,420 fund-year portfolio holdings
that cover 499 mutual fund families (companies) with a
total of 1,904 funds. Each mutual fund family has on average four different funds. While some families sell the same
portfolio to investors under slightly different names depending on their fee structure and minimum investment
requirements, we consider these different funds with identical portfolios only once (we do not treat them as separate
funds). The total number of asset-level observations in our
data set is 1,359,750, counting each stock-level allocation
across all of the funds over time.
We also collect the time series of mutual fund returns.
Because these are open-end funds, the value of each fund
each day (or net asset value, NAV) reflects the value of its
underlying holdings. To be able to compare returns across
funds within families, we restrict our focus to large families
with several types of funds. We thus use daily returns at the
fund level between September 1989 and June 2006 for 36
mutual fund families. We work with a total of 722,885 daily
observations that comprise all of the returns for all of the
funds in our sample. We include all funds within a given
family. On average, each family in the sample has ten distinct mutual funds.6
III.
How Do Mutual Funds Allocate Their Portfolios
Globally?
The U.S. mutual fund industry’s activity in international
markets has expanded sharply since the early 1990s. For
example, in 1991 there were fewer than 170 mutual funds
established to invest in international equity, while in 2005
there were almost 700 funds (490 global). The number of
global funds increased steadily until the early 2000s. Relative to global funds, specialized funds were important initially, increased until 1998, and declined afterward (figure 2,
panel A). The differences are even starker in terms of assets
under management. Global (specialized) funds managed
$29 ($7) billion in 1991 and $781 ($160) billion in 2005.
The data show a clear trend in favor of the funds with a
wider investment scope relative to the funds that invest in
specific regions or countries.7
As the investment scope expands, do mutual funds hold
more assets across more countries? Table 1 (top panel) pre6
See the working paper version of this paper, Didier, Rigobon, and
Schmukler (2010), and the online appendix for more details on the collection, construction, and features of the data.
7
The increase in the number (and total assets) of global funds might be
driven by a desire to have funds that can invest more freely around the
world, while giving investors a unique global portfolio. Moreover, mutual
fund families have incentives to offer a broad range of funds to investors.
A greater number of funds allow companies to differentiate their products
and likely expand their assets under management and their revenues. Different funds also give investors more flexibility to invest internationally
according to their preferences and constraints.
1565
sents the average, the median, and the standard deviation of
the number of holdings across the different mutual fund
types over the entire 1991–2005 period. The table shows
that the median number of holdings for world funds is 106
stocks and for foreign funds is 105 stocks, while the median
for emerging market funds is 121 stocks. The medians for
the more specialized Europe and Asia funds are 71 and 65
stocks, respectively, while those for Latin America and
country funds are 56 and 63 stocks, respectively. The number of asset holdings in the mutual fund portfolios does not
tend to be higher for global funds than for specialized
funds, even though the pool of investable assets is significantly larger for global funds. Moreover, the median number of stock holdings for the different mutual fund types is
very stable over the fifteen-year period and not very different across fund types (figure 2, panel B). In other words, the
data suggest that mutual fund managers tend to invest in a
limited number of stocks that does not increase significantly
as the investment scope widens, even as the amount of
money these funds manage rises markedly over time.
Do global funds hold fewer assets from fewer countries
in each region than specialized funds within the same
mutual fund family? The results in table 2 show that this is
the case. In fact, global funds hold significantly fewer
stocks and countries. For example, emerging market funds
hold on average 34% fewer assets in Latin America than
Latin America funds, whereas foreign and world funds hold
93% and 94% fewer assets in this region, respectively.
Moreover, the median number of countries is six in Latin
America fund portfolios, whereas the median number of
countries falls to less than two in global fund portfolios. We
observe similar trends for Asia and Europe.
Are the holdings across countries related to funds investing in different economic sectors? Using the funds’ own
reporting, we classify stocks as belonging to one of the following sectors: consumer goods, financial services, health,
industrial, services, technology, and utility.8 We compute
the asset allocation for each type of fund in these different
sectors and calculate the median allocation across funds.
The results show that the asset allocations across these
sectors are almost identical for global and specialized funds
as well as across the different fund subtypes (table 3).
Thus, the patterns of portfolio holdings across global and
specialized funds are difficult to attribute to different sectoral allocations. This result is robust to a number of (unreported) alternative specifications, including the use of
averages instead of medians, portfolio loadings in each sector instead of the number of stocks, and different definitions
of the sectors (classifying stocks homogeneously across
funds over time or using the Standard Industrial Classification (SIC)).9
8
If a fund does not identify a sectoral classification for a particular
holding, we assign the classification most cited by other funds in our sample, which allows us to classify 96% of the stock holdings in our data.
9
See the online appendix.
1566
THE REVIEW OF ECONOMICS AND STATISTICS
FIGURE 2.—NUMBER OF FUNDS, ASSETS UNDER MANAGEMENT, AND NUMBER OF HOLDINGS
A. Total Number of Funds and Total Assets under Management
900
600
800
500
700
600
500
300
400
US$ Billion
No. of Funds
400
300
200
200
100
100
0
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
0
2005
No. of Global Funds
No. of Specialized Funds
Assets under Management of Global Funds (RHS)
Assets under Management of Specialized Funds (RHS)
B. Median Number of Holdings
All Funds
160
No. of Stock Holdings
140
120
100
80
60
40
20
0
1991
1992
1993
1994
1995
1996
World Funds
Foreign Funds
Regional Funds
1997
1998
1999
2000
2001
2002
2003
2004
World Funds - Excluding U.S. Holdings
Emerging Market Funds
2005
2000
2005
Specialized Funds
160
140
No. of Stock Holdings
120
100
80
60
40
20
0
1991
1992
1993
1994
Asia Funds
1995
1996
1997
Europe Funds
1998
1999
2001
Latin America Funds
2002
2003
2004
Country Funds
This figure shows the evolution of the total number of mutual funds (panel A), the total value of assets under management (panel A), and the median number of stock holdings by fund type (panel B) in our holdings
database from 1991 to 2005. Global funds comprise world and foreign funds. Specialized funds comprise emerging market, regional, and country funds.
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1567
TABLE 1.—NUMBER OF MUTUAL FUND HOLDINGS
Fund Type
Average
Median
SD
155
136
101
175
117
161
89
111
58
126
150
96
106
76
105
79
121
65
71
56
63
95
196
132
100
219
136
138
110
158
24
178
186
Global funds
World funds
Excluding the U.S. holdings
Foreign funds
Specialized funds
Emerging market funds
Asia funds
Europe funds
Latin America funds
Country funds
All funds
Dispersion in the Number of Mutual Fund Holdings
Median Number of Holdings by Mutual Fund Family
1,200
1,100
No. of Stock Holdings
1,000
900
800
First
Quintile
Second
Quintile
Third
Quintile
Fourth
Quintile
Fifth
Quintile
Average: 39
Max: 56
Average: 67
Max: 77
Average: 89
Max: 102
Average: 122
Max: 153
Average: 335
Max: 1,094
700
600
500
400
300
200
100
0
Families
The table in the top panel shows the average, the median, and the standard deviation of the number of stock holdings by fund type across all mutual funds over the 1991–2005 period. The figure in the bottom panel
shows the dispersion in the number of stock holdings across mutual fund families. It shows the median number of stock holdings across all funds within each mutual fund family over the 1991–2005 period. All of
the funds in any given family are considered for this figure. The families are then divided into five groups (quintiles). The average and maximum values for each quintile are reported.
TABLE 2.—DIFFERENCES IN HOLDINGS WITHIN REGIONS BY FUND TYPE
Number of Stocks
Fund Type: Regional Funds
Asia
Developed Europe
Median number of holdings
60
62
Drop in the number of stocks in each region by fund type (in percent, relative to regional funds)
Emerging market funds
33%
–
Foreign funds
42%
5%
World funds
69%
49%
Number of Countries
Fund Type: Regional Funds
Asia
Developed Europe
Median number of countries
8
12
Drop in the number of countries in each region by fund type (in percent, relative to regional funds)
Emerging market funds
10%
–
Foreign funds
30%
0%
World funds
36%
14%
Latin America
41
34%
93%
94%
Latin America
6
17%
72%
75%
This table reports the differences in the regional portfolio allocations across fund types within mutual fund families over the 1997–2005 period. The top panel shows the differences in the number of stock holdings
within each region across fund types. The bottom panel shows the differences in the number of countries receiving investments within each region across fund types. The first row within each panel reports the median
number of stocks/countries in a given region that regional funds hold. The drop in the number of stocks/countries is calculated as the percentage change between the median number of stocks/countries held by emerging market, foreign, or world funds relative to regional funds. The comparisons are conducted within mutual fund families.
IV.
What Factors Might Explain the Global Portfolio
Allocations?
A. Asset Availability and Transaction Costs
As a first step to understanding why, as their investment
scope broadens, mutual funds invest larger amounts in fewer
stocks and countries within each region of exposure, we analyze the universe of investable assets. Table 4 reports the
number of listed stocks across different regions in 1997 and
2004. The table also reports the actual number of mutual
fund holdings and the percentage of holdings relative to the
number of listed companies. In 1997, mutual funds invested
in about 9,000 different firms from around the world. In
1568
THE REVIEW OF ECONOMICS AND STATISTICS
TABLE 3.—ALLOCATION OF THE MUTUAL FUND HOLDINGS ACROSS SECTORS
Median Portfolio Allocation
Fund Type
Number of
Classified Holdings
Consumer
Goods (S1)
Financial
Services (S2)
Health
(S3)
Industrial
(S4)
Services
(S5)
Technology
(S6)
Utility
(S7)
88
63
96
69
106
56
64
42
75
81
14%
15%
14%
13%
13%
13%
13%
14%
6%
14%
20%
18%
20%
20%
20%
22%
22%
14%
17%
20%
6%
6%
6%
3%
2%
2%
8%
0%
2%
6%
16%
15%
17%
16%
19%
14%
14%
21%
23%
16%
19%
20%
19%
19%
17%
19%
19%
26%
21%
19%
8%
8%
8%
9%
10%
13%
7%
0%
12%
8%
13%
12%
13%
15%
18%
11%
14%
18%
19%
13%
Global funds
World funds (excluding U.S. holdings)
Foreign funds
Specialized funds
Emerging market funds
Asia funds
Europe funds
Latin America funds
Country funds
All funds
Cumulative Distribution of the Number of Holdings
Median across Funds
1.00
0.90
0.80
0.70
0.60
0.50
0.40
Global Funds
0.30
Specialized Funds
0.20
0.10
0.00
S1
S2
S3
S4
Sectors
S5
S6
S7
The top panel of the table shows the median portfolio allocation across the different sectors by mutual fund type over the 1997–2005 period. The portfolio allocations are based on the number of stock holdings.
The bottom panel shows separately the median cumulative distribution of the stock holdings across sectors for global and specialized funds. The sectoral classification of the mutual fund holdings follows the funds’
own classification. If a particular fund holding is not classified by the reporting fund, we assign the most cited classification for that asset by other funds in our sample.
TABLE 4.—MUTUAL FUND HOLDINGS
All Fund Holdings
Number of
Listed Stocks
Number of
Holdings
Total
Developed countries
Asia
Europe
Middle East
Developing countries
Asia
Europe
Latin America
Middle East and Africa
30,319
12,987
5,760
6,392
802
17,332
10,089
2,697
2,196
2,350
9,086
6,815
3,249
3,459
87
2,271
1,304
319
399
249
Total
Developed countries
Asia
Europe
Middle East
Developing countries
Asia
Europe
Latin America
Middle East and Africa
39,061
18,282
7,758
9,817
686
20,779
10,444
6,279
1,525
2,531
6,289
5,204
2,748
2,392
45
1,085
566
184
195
140
As a Percentage
of Listed Stocks
Global Fund Holdings
Number of
Holdings
As a Percentage
of Listed Stocks
A. 1997
30%
52%
56%
54%
11%
13%
13%
12%
18%
11%
6,267
4,953
2,246
2,635
54
1,314
693
167
297
157
21%
38%
39%
41%
7%
8%
7%
6%
14%
7%
B. 2004
16%
28%
35%
24%
7%
5%
5%
3%
13%
6%
5,510
4,799
2,429
2,315
37
711
394
114
141
62
14%
26%
31%
24%
5%
3%
4%
2%
9%
2%
This table shows the numbers of listed stocks and stock holdings by mutual funds in developed and developing countries across the selected regions. The top panel shows the data for 1997 the bottom panel for
2004. The first column shows the number of listed stocks across the countries’ main stock exchanges within each region. The second and third columns show the number of stock holdings in these regions by all of
the mutual funds in our sample, in absolute terms and as a percentage of the number of listed stocks. The fourth and fifth columns report the same statistics but consider the portfolio holdings of global funds only.
The data on the number of listed stocks come from the Global Financial Database. We exclude the stock holdings in the United States and in offshore financial centers from this analysis.
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1569
FIGURE 3.—MUTUAL FUND HOLDINGS AS A PROPORTION OF THE TOTAL NUMBER OF LISTED STOCKS BY COUNTRY
100%
90%
80%
First Quintile
Second Quintile
Third Quintile
Fourth Quintile
Fifth Quintile
Average: 1.1%
Max: 2.4%
Average: 7.7%
Max: 13.8%
Average: 21%
Max: 27.6%
Average: 34.8%
Max: 43.6%
Average: 57.8%
Max: 77.3%
70%
60%
50%
40%
30%
20%
10%
Nigeria
Saudi Arabia
Romania
Lithuania
Latvia
Slovak Republic
Bangladesh
Bulgaria
Tunisia
Iceland
Oman
Jordan
Cyprus
Pakistan
Egypt
India
Croatia
Uruguay
Slovenia
Ecuador
Sri Lanka
Peru
Colombia
Kazakhstan
Estonia
Zimbabwe
Chile
Czech Republic
Spain
Israel
Panama
Venezuela
Morocco
Kenya
Botswana
South Africa
Lebanon
Brazil
Poland
Canada
Philippines
Russia
All China*
Australia
Indonesia
Mauritius
Turkey
Thailand
Malaysia
Greece
South Korea
Portugal
Ghana
Argentina
Germany
Hungary
Mexico
Norway
France
United Kingdom
Austria
Singapore
Denmark
Belgium
New Zealand
Finland
Switzerland
Sweden
Japan
Italy
Ireland
Netherlands
0%
This figure shows the percentage of the listed stocks that receive investments from mutual funds. Countries are sorted according to their average percentage over the 1997–2004 period. Countries are divided into
quintiles. The figure reports the average and maximum values for each quintile. The United Sates is excluded from the figure, along with other countries with no data on the total number of listed stocks. The data for
the total number of listed stocks come from the Global Financial Database.
*‘‘All China’’ includes assets in the following economies: mainland China, Hong Kong, and Taiwan.
developed countries, they held on average 52% of the listed
assets, whereas in developing countries, they held only 13%
of the listed stocks. A more pronounced pattern is observed
when considering only global funds, which became very
large over the sample period. In 1997, global funds held 38%
(8%) of the number of stocks in developed (developing)
economies. Table 4 also shows that although the universe of
listed companies increased between 1997 and 2004, there is
a considerable decline in the number of mutual fund holdings. This decline is not concentrated in any particular region
but is more accentuated in developing countries, where we
observe a fall of 52% in the asset holdings.
Although the overall number of different mutual fund
holdings fell between 1997 and 2004, the amount invested
in the stocks held grew significantly. The investments in
developed countries rose from $204 billion in 1997 to $446
billion in 2004. In developing countries, they increased
from $30 billion to $62 billion. Thus, a growing amount of
funds is being invested in fewer firms, more significantly so
in developing countries.
To complement the evidence that mutual fund investments are concentrated in a few companies, figure 3 illustrates how mutual funds invest across countries. The figure
plots the ratio of the number of companies held in the
mutual fund portfolios to the total number of listed companies across countries. These ratios are computed on a yearly
basis and reported according to their averages over the
entire 1997–2004 period. The figure shows that the mutual
fund holdings are not spread evenly across countries. For
around half of the countries in the sample, mutual funds
invest in at most 20% of the listed companies. In no country
do mutual funds exhaust the number of listed stocks. Only
developed countries appear in the highest quintile.
Transaction costs could be an impediment to the expansion
in the number of stocks in the mutual fund portfolios because
not all of the listed stocks can be bought at a relatively low
cost. However, the cross-fund comparison is revealing and
suggests that even when present, transaction costs do not
seem to constitute a strong binding constraint. Specifically,
the fact that specialized funds hold more stocks than global
funds within each region of exposure is an indication that
there are no clear investment restrictions related to those
companies. Global funds could thus expand the range of their
investments by simply purchasing the same stocks that specialized funds hold. The same applies to the stocks that global
funds hold and specialized funds do not. Furthermore, mutual
funds hold a small fraction of the listed stocks. Although the
case could be that market thinness plays a role, both types of
funds typically invest in the largest firms in each country, and
their holdings are small relative to the firms’ market capitalization (on average, 0.12% of the firms’ market capitalization). Moreover, though the firms held by global funds are
typically larger than those held by specialized funds, no significant difference exists in their liquidity.10
In sum, neither the lack of available assets nor transaction costs (broadly understood as the ability to purchase
stocks) appear to strongly determine the portfolio choices
of mutual funds.
B. Stock Commonality
If global and specialized funds within mutual fund
families share information and make similar decisions, one
might expect to observe similar portfolios across them. To
the extent that information is costly to obtain and process,
the managers of global funds might benefit from the information that the managers of specialized funds already have.
10
See Didier (2011) for the differences in the underlying liquidity of
the mutual fund stock holdings across fund types and the online appendix
for the size of the mutual fund holdings relative to market capitalization.
1570
THE REVIEW OF ECONOMICS AND STATISTICS
In particular, the managers of specialized funds need to
decide on an asset allocation in their particular countries or
regions, and in doing so they are likely to collect specific
information that the managers of global funds might use. On
the other hand, if managers compete with each other and
each manager gathers his or her own information, one will
observe dissimilar portfolios across funds within families.
From the evidence presented earlier, we know that global
funds do not hold the same portfolios as specialized funds;
they hold fewer stocks within each region. But we do not
know whether the stocks picked are actually a subset of those
held by specialized funds. The within-family comparison is
particularly important given a large heterogeneity in the
holdings across mutual fund families and given the interest
in whether managers in the same company make similar
decisions as a sign of information sharing.
To assess the similarity in the portfolios, we first compute frequency counts. We consider the global and specialized funds within a mutual fund family and count the number of observations for which a stock is held by either one
of these two fund types, with each of the almost 400,000
observations being a family-year-stock observation. Then,
we compute the fraction of the observations in which a
stock is held (a) by one fund type but not the other, (b) by
both fund types, and (c) by the global fund when there is no
specialized fund within the same family that could hold that
stock. We make these comparisons within each year. By
construction, for every specialized fund, there is always a
global fund within the mutual fund family.11 Also by construction, there are no observations for which a stock is held
by neither a global nor a specialized fund.
Table 5 shows the results. The numbers in the table report
the relative frequency of the observations, that is, the joint
probability that global and specialized funds hold or do not
hold a particular stock. The conditional probabilities can be
obtained by looking at a particular row or column. The table
shows that global and specialized funds do not hold many
stocks in common. Only 16% of the actual holdings are
shared by both fund types. Of the global fund holdings, only
23% are shared by specialized funds. Moreover, 32% of the
stocks are held by specialized funds alone but not by global
funds. Unreported results show that 75% of the mutual fund
investments in developing countries are held by specialized
funds. Conditional on being held by a specialized fund, there
is only a 15% probability that a stock from a developing
country is held by a global fund. Therefore, global and specialized funds seem to invest in different firms.12
11
We exclude all of the stock observations for mutual fund families that
do not have one of the fund types in a given year. We also exclude the
U.S. stocks from this analysis.
12
In the online appendix, we split the sample by considering the holdings only in developing countries and obtain qualitatively similar patterns.
In the working paper version of this paper (Didier et al., 2010), we further
split global funds into world funds and foreign funds and compare them
with specialized funds. World funds and specialized funds share only
10% of their holdings. This percentage increases to 15% when we use foreign funds.
TABLE 5.—PROBABILITIES OF BEING HELD BY A MUTUAL FUND
Global Funds
Probability of:
Specialized funds
Probability of:
Not being held
Being held
No specialized fund
Total (number of observations)
Not Being
Held
Being
Held
0%
32%
0%
32%
25%
16%
27%
68%
Total
25%
48%
27%
100%
(396,388)
This table shows a two-way frequency count for the mutual fund stock holdings from 1997 to 2005.
The reported numbers correspond to the joint probability of a stock being held by a specialized fund and
a global fund in a given year, conditional on a family having both fund types. Each observation is a
family-year-stock observation. The total number of observations is reported in parentheses. When a global fund in a given family-year holds a stock in a country not covered by the specialized funds within
that family in that year, this observation is counted in the ‘‘No specialized fund’’ row. For this analysis,
we use all stock holdings, except the U.S. stocks. Global funds comprise both world and foreign funds.
Specialized funds comprise emerging market, regional, and country funds.
While the frequency counts measure to what extent
mutual funds with different investment scopes hold similar
assets, they do not consider the value of the mutual fund
investments in each stock. To account for the possibility
that global and specialized fund portfolios contain large
loadings on common stocks (even when the range of stocks
in which they invest differs), we study entropy measures
that capture how alike the mutual fund investments actually
are. The measure is
P
P
j
i
s;i NAVs; f ;t þ
s; j NAVs; f ;t
i; j
;
ð1Þ
Entropyf ;t ¼ P
P
j
i
i NAVf ;t þ
j NAVf ;t
where Entropyi;f ;tj is calculated for all funds within
types i and j for family f at time t, i; j 2 fglobal fund,
specialized fundg and s are stocks common to the portfolio
of both funds i and j from family f at time t. The measure is
constructed within families for every family in every year.
For a given pair of different fund types within the same
mutual fund family, this entropy measure is the ratio of the
sum of the dollar investment (NAV) in stocks common to the
portfolio of these two fund types over the sum of the total net
assets of the same funds. This ratio can be regarded as an
upper bound of commonality because it compares global
funds to aggregates of all specialized funds within families.
The entropy measure indicates that global and specialized
funds do indeed hold more similar portfolios than what the
frequency counts suggest (figure 4, top panel), though they
still invest in quite different portfolios. For example, the
entropy measure shows that, on average, 36% of the value
of their holdings is in common assets, while the number of
their holdings suggests a commonality of only 16% (table
5). Moreover, the entropy measure is stable over the sample
period and, if anything, it has decreased since 2001.
Interestingly, this commonality measure increases substantially with the number of common managers across
funds within mutual fund families (figure 4, bottom panel).
For example, the median entropy for the families in which
funds have no common manager is 29%, while the median
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1571
FIGURE 4.—ENTROPY
Within-Family Entropy
1.00
0.90
0.80
0.70
0.60
0.50
Median Entropy
0.40
0.30
0.20
0.10
0.00
1997
1998
1999
2000
2001
2002
2003
2004
2005
Within-Family Entropy by Number of Common Managers
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0.00
1997
1998
1999
2000
2001
2002
2003
2004
Entropy
No Common Manager
At least 1 Common Manager
More than 3 Common Managers
2005
This figure shows in the top panel the within-family entropy measure for stock holdings from 1997 to 2005. The entropy measure captures the commonality of stock holdings in the portfolios of funds within a
mutual fund family. The thick line represents the median value of the entropy measure across mutual fund families in a given year, while the dotted gray lines represent þ/ 1 standard deviation from the median.
The bottom panel shows the entropy measure from 1997 to 2005 according to the number of common managers shared by funds within mutual fund families. The entropy measure is calculated separately for the
family-year observations in which the global and specialized funds share no managers, have at least one common manager, and have more than three common managers. For comparative purposes, the bottom panel
of this figure also reports the same entropy measure (black-dashed line) reported in the top panel of the figure. For the calculation of the entropy measures, we use all stock holdings, except the U.S. stocks.
entropy for the family-years with at least one common manager across different funds is 43%, and the one with more
than three common managers is 65%. Furthermore, the
number of common managers is statistically significant and
positively related to the entropy measure (table 6). As the
number of common managers across funds within families
increases, so does the degree of commonality in the mutual
fund portfolios.
C. Family Effects
We next analyze the role of family effects in explaining
portfolio choices.13 Our data show a significant dispersion
in the number of stock holdings. For instance, 73% of the
13
We follow the organizational literature that emphasizes the importance of firm effects (as opposed to plant effects within firms) to understand corporate behavior. Much of this literature (e.g., Henderson &
Cockburn, 1994; Klette, 1999) studies the existence of firm effects
(family effects in our paper) through firm-level dummies and measures
their relevance by the increase in the R2 of the regressions. Analogously,
Bertrand and Schoar (2003) analyze the impact of managerial effects on
corporate policies and performance.
observations correspond to portfolios with fewer than 150
stocks, whereas 9% of the observations represent portfolios
with more than 350 stocks. This dispersion in the number
of stocks in the fund-year observations is linked to the variance in the number of stocks held across mutual fund
families. In fact, mutual fund families differ substantially in
the number of stocks their mutual funds hold in their portfolios. For example, funds that belong to GAM Funds and
Oppenheimer Funds hold on average substantially fewer
than 200 stocks, while funds in other families like Dreyfus
Founders and Vanguard Group hold about twice as much.
The bottom panel of table 1 shows the sorted median number of stocks in the mutual fund portfolios across families.
The mean of the first quintile of the distribution is 39
stocks, whereas the mean of the fifth quintile is 335.
Although extreme cases exist, funds in most families hold a
limited number of stocks.14
14
The working paper version of this paper (Didier et al., 2010) and the
online appendix show the dispersion in the number of holdings across
mutual funds.
1572
THE REVIEW OF ECONOMICS AND STATISTICS
TABLE 6.—COMMONALITY IN HOLDINGS ACROSS FUND TYPES
Dependent Variable: Entropy Measure
Independent variables
Number of common managers
(1)
(2)
0.061***
[0.006]
0.059***
[0.006]
No common manager (NCM0)
One common manager (NCM1)
Two common managers (NCM2)
At least three common managers (NCM3)
Year dummies
Number of observations
R2
Adjusted R2
T-tests:
NCM0 ¼ NCM1
NCM0 ¼ NCM2
NCM0 ¼ NCM3
No
370
0.15
0.15
Yes
370
0.18
0.16
(3)
(4)
0.292***
[0.018]
0.362***
[0.034]
0.421***
[0.031]
0.543***
[0.035]
No
370
0.69
0.68
0.207***
[0.042]
0.284***
[0.052]
0.329***
[0.049]
0.456***
[0.052]
Yes
370
0.70
0.69
3.390*
13.190***
40.800***
4.060**
11.050***
42.230***
This table reports the regressions of the within-family entropy measure of stock holdings on the number of common managers and, alternatively, on the dummy variables that indicate whether funds within a
family-year share no common manager or one, two, or at least three common managers. The entropy measure captures the commonality of stock holdings in the portfolios of funds within mutual fund families. The
sample period is from 1997 to 2005. The t-tests of equality of the estimated coefficients on the dummy variables capturing the number of common managers are also reported. For this analysis, we use all stock holdings except the U.S. stocks. Standard errors are clustered at the family level. Standard errors are shown in brackets. Significant at ***1%, **5%, and *10%.
In table 7, we test more formally the importance of
family effects in explaining both the number of stock holdings (a measure of portfolio breadth) and the portfolio loadings on the top ten holdings (a measure of portfolio concentration). Panel A shows the R2 from the regressions of each
of these variables on year, fund type, and family dummies.
The year dummies explain just 1% of the variance in the
mutual fund holdings or the top ten holdings. The fund type
dummies explain only 2% of the variance in the number of
holdings and 11% of the variance in the top ten holdings. In
contrast, family dummies explain 46% of the variance in
the number of holdings and 36% of the variance in the top
ten holdings across funds and over time, much greater percentages than those explained by fund type and year effects
alone.15 When combining these three types of dummies, the
R2 is relatively large only when the family dummies are
included. When all dummies are included, there is only a
slight increase in the R2 in comparison to the other regressions with family dummies. Therefore, family effects indeed
seem relevant to the portfolio decisions of mutual funds by
affecting both the number of stock holdings and the allocation in the top holdings.
The importance of family effects raises the immediate
question of which factors might be behind the observed patterns. To shed light on these family effects, and in line with
the organizational literature, we estimate regressions similar
to those in panel A of table 7 but controlling for other variables believed to fundamentally affect the portfolio choices
of mutual funds. In particular, we explore the relevance of
15
This increase in the variance explained is not due to the increase in
the number of dummies since the adjusted R2 also rises significantly.
family-level and fund-level variables. We relate the number
of stock holdings and loadings on the top ten stocks to (a)
the ability of funds to gather and process information
(approximated by the number of managers, family expenses, and family size), (b) variables related to the characteristics of funds and their managers that could also affect
portfolio decisions (fund age, manager tenure, and fund
type fixed effects), and (c) family effects themselves, which
capture any remaining attribute or practice at the family
level.16 The first set of variables directly captures the extent
to which costly information is a binding factor in driving
portfolio decisions.
The results in panel B of table 7 show that the number of
managers and family size are positively associated with the
number of holdings, while expenses at the family level
show a negative correlation.17 Although statistically significant, these variables explain only a small proportion (5% to
7%) of the variance in the number of stocks held, versus the
49% explained when family dummies are included. Moreover, when family dummies are present, not only does the
R2 increase considerably, but also some of the fund- and
family-level variables become statistically not significant.
The regressions on the top ten holdings yield similar
results.
16
The working paper version of this paper (Didier et al., 2010) reports
regressions with fund-level (instead of family-level) variables to capture
the funds’ ability to gather and process information. The results are qualitatively similar to the ones shown here.
17
Unreported results (available in the online appendix) show that funds
with one manager hold an average of 133 stocks, funds with two managers average 135 stocks, and funds with six managers average 197
stocks.
Yes
Yes
No
6,093
0.05
0.05
14.762***
[4.569]
1.468
[2.255]
0.316
[0.845]
0.650**
[0.252]
7.535***
[2.786]
Yes
Yes
No
6,093
0.07
0.07
No
Yes
No
6,394
Yes
No
No
6,394
16.180***
[4.655]
2.964
[2.488]
0.211
[0.775]
0.02
0.02
0.01
0.01
(2)
(4)
(5)
Yes
Yes
Yes
6,093
0.49
0.45
4.693
[3.702]
2.260*
[1.208]
1.027
[0.863]
No
No
Yes
6,394
4.601
[3.703]
2.243*
[1.203]
1.013
[0.863]
0.014
[0.160]
0.575
[1.543]
Yes
Yes
Yes
6,093
0.49
0.45
Yes
Yes
No
6,080
0.13
0.12
0.554***
[0.175]
0.067
[0.118]
0.129**
[0.053]
Yes
Yes
Yes
No
Yes
No
6,394
6,379
B. Importance of Family Effects
A. Importance of Year, Fund Type, and Family Dummies
0.46
0.48
0.01
0.42
0.44
0.01
(3)
0.529***
[0.178]
0.033
[0.115]
0.106**
[0.052]
0.001
[0.011]
0.062
[0.110]
Yes
Yes
No
6,080
0.13
0.13
No
Yes
No
6,379
0.11
0.11
(6)
Yes
Yes
Yes
6,080
0.45
0.41
0.186
[0.188]
0.133
[0.084]
0.126**
[0.049]
No
No
Yes
6,379
0.36
0.32
(7)
0.179
[0.187]
0.129
[0.084]
0.128***
[0.049]
0.010
[0.009]
0.053
[0.088]
Yes
Yes
Yes
6,080
0.45
0.41
Yes
Yes
Yes
6,379
0.44
0.40
(8)
This table reports the regressions of the number of stock holdings (left four columns) and the percentage of net assets in the top ten stock holdings (right four columns) on year dummies, fund type dummies, or family dummies (panel A), and the number of managers, manager
tenure, mutual fund age, mutual fund family expenses, and mutual fund family size (panel B). Depending on the specification, year, fund type, or family dummies are included in the regressions, although the estimated coefficients on these dummies are not reported. Family
expenses are measured in millions of U.S. dollars, and family size is measured in billions of U.S. dollars. Fund age is measured in years. The sample period for the regressions in both panels is 1997 to 2005. Each data point is a fund-year observation. The standard errors are clustered at the family level. The standard errors are in brackets. Significant at ***1%, **5%, and *10%.
Year dummies
Fund type dummies
Family dummies
Number of observations
R2
Adjusted R2
Family size
Family expenses
Fund age
Manager tenure
Independent variables
Number of managers
R2
Adjusted R2
Independent variables
Year dummies
Fund type dummies
Family dummies
Number of observations
(1)
Dependent Variable: Percentage of Net Assets in the Top Ten Holdings
TABLE 7.—PORTFOLIO CHOICE OF MUTUAL FUNDS: IMPORTANCE OF YEAR, FUND TYPE, AND FAMILY EFFECTS
Dependent Variable: Number of Stock Holdings
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1573
1574
THE REVIEW OF ECONOMICS AND STATISTICS
In sum, the evidence presented thus far indicates that the
factors typically emphasized in the literature such as asset
availability, transaction costs, and common managers are
not able to account for the patterns in the portfolio allocations. There is in fact a strong family effect beyond fundamentals that explains these holdings, which suggests that
industrial organization factors might be important.
V.
Returns to Diversification
The fact that global funds tend to hold fewer stocks from
fewer countries than specialized funds within their regions
of exposure might be explained by the lack of potential
diversification gains (due to correlated returns) or by the
desire of investors to minimize tail risk, or both. We
explore these effects next.
A. Standard Portfolio Model: Mean-Variance Analysis
To evaluate whether global funds seem to forgo potential diversification gains, we compare the returns of global
funds to those of what we call simulated global funds. We
construct one simulated global fund for each actual global
fund that consists of a portfolio of the specialized funds
from the same mutual fund family and the global fund
itself. This simulation is analogous to letting a global fund
invest in a portfolio that replicates the holdings of specialized funds at any point in time. The portfolio weights on
the specialized funds and the global fund itself are obtained through mean-variance optimizations. The returns
of the simulated global funds are compared to the returns
of the actual global funds over the same period. This comparison is a conservative exercise to evaluate the potential
gains from international diversification because it does not
use all of the stocks in the investment universe of global
funds to construct the alternative portfolios (which might
include assets that are hard to reach but could yield substantially higher risk-adjusted returns). Our comparison
uses only the stocks already chosen by the specialized
funds within the same family.18 The fact that at least one
specialized fund is already holding an asset is an indication that this asset is within the subset of investable assets
and that the family has already paid for the potential costs
of collecting and processing information related to that
stock.
To perform the mean-variance analysis, consider a global
fund with an observed return history G and several specialized funds within the mutual fund family of the global fund
with observed returns Si . The global fund can invest anywhere in the world, including the assets held by the specia18
While this exercise is informative for our purposes, it differs from
many others conducted in the literature. In fact, there is a very broad literature that discusses optimal portfolios with different goals in mind,
mostly using U.S. data. See, for example, Evans and Archer (1968) and
DeMiguel, Garlappi, and Uppal (2009).
lized funds, whereas the specialized funds invest in specific
regions. The simulated global fund is constructed as a portfolio P that assigns nonnegative weights to the global fund
itself and to all of the specialized funds within the same
mutual fund family. This within-family exercise is isomorphic to allowing a global fund to invest in the specialized funds within its mutual fund family. This portfolio P
is constructed such that it maximizes risk-adjusted returns
by either minimizing its variance and achieving at least the
same expected return as the global fund itself or maximizing its expected returns conditional on not increasing the
return volatility (relative to the actual global fund).
In sum, we impose the following restrictions to construct
the simulated global funds: (a) the portfolios are constructed for each global fund using a combination of the
fund itself and the specialized funds within the same mutual
fund family; (b) only buy and hold strategies are considered
(funds cannot be shorted); (c) the performance evaluation is
always conducted out of sample; (d) the portfolio is optimized by using alternatively the historical daily, weekly, or
monthly information; and (e) a mean-variance framework is
used.
The first optimization problem minimizes the variance of
the returns of the simulated global fund, keeping its returns
at least as large as those of the actual global fund. The exercise can be described as
P
Minx VarðPÞ ¼ x0 x;
such that
EðPÞ EðGÞ; 0 xi 1; Ri xi 1;
and
P ¼ ð1 Ri xi Þ G þ Ri xi Si ;
ð2Þ
where xi is the portfolio weight on the specialized fund i
within the mutual fund family of the global fund and S is
the variance-covariance matrix (VCM) of all mutual fund
returns within the same family.19 Because the simulated
global fund P is evaluated out of sample, the portfolio
shares are computed at time t using all available information up to that time and held for the next period, when the
return of P is computed. We then compare the return of the
simulated global fund P with the return of the global fund
G. The portfolio weights are actively reoptimized every
period.
We also maximize expected returns, keeping the variance
of the simulated global fund from being larger than that of
19
We estimate the VCM at every point in time using past return data on
mutual funds themselves, not return data at the stock level. This method
has the advantage of working with a very limited set of returns: those
from the relevant specialized funds within a given family and one from
the global fund that we intend to improve. More specifically, our simulations use between a median of five funds (longest available sample simulation) and seven funds (largest number of funds simulation). This limited
number of return time series is important because problems of instability
in the estimation of VCMs usually arise when the number of stocks
increases at the same speed as the sample size.
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
the global fund itself. This strategy can be described as follows:
Maxx EðPÞ;
such that
VarðPÞ VarðGÞ; 0 xi 1; Ri xi 1;
and
P ¼ ð1 Ri xi Þ G þ Ri xi Si :
ð3Þ
We perform these exercises for several types of global
funds: world funds, foreign funds, and pools of world or
foreign funds. The pools of world (or foreign) funds exist
when more than one fund in a mutual fund family is classified as a world (or foreign) fund and they have different natures (for example, value, growth, or blend funds). A benefit
of this kind of exercise is that it requires information only
on mutual fund returns (not individual stock returns) and
the investment scope of funds.
Table 8 shows the results, comparing the simulated and
actual global funds. The left panel of the table reports the
results for the simulated global funds constructed with the
largest number of available specialized funds (the largest
cross-section), called the ‘‘largest number of funds’’ simulation. This simulation includes all of the possible specialized
funds for each family and adjusts the time series accordingly to use the sample available for all of the funds
included in the simulation. The right panel of table 8 reports
the results with only the specialized funds that allow for
estimations of the simulated global funds with a relatively
long time series, called the longest available sample simulation. In particular, specialized funds are excluded from
the simulations if they reduce the sample size by at least
six months. On average, three specialized funds are excluded from these simulations relative to the simulations of
the largest number of funds, which leads to an average
increase of 44 months in the time span of the simulations.
We compute the annualized differences in the returns
between the simulated global funds and the global funds
over the entire sample period for each simulation and then
the averages across the simulations.20 The results are shown
for daily, weekly (measured on Wednesday), and monthly
returns.
The results show that when minimizing variances with
daily data, the simulated global funds yield on average
annualized excess returns of 485 basis points per year relative to the world funds, 403 basis points relative to the foreign funds, and 455 basis points relative to the pool of
world or foreign funds. Moreover, the daily standard deviations of the returns of the simulated global funds are also
smaller than those of the global funds. For example, the
standard deviation falls by 8 basis points for the world and
foreign funds and 7 basis points for the pool of world or for20
The working paper version of this paper (Didier et al., 2010) has
results at the family level to show the heterogeneity in the estimates.
1575
eign funds. The results hold when using weekly and
monthly returns. The simulated global funds yield on average 436 (275) basis points more per year than the actual
global funds when considering all types of global funds
with weekly (monthly) data. The smaller point estimates
are expected because the optimization methods use less
information at lower data frequencies. The results are similar in the simulations with the longest time span. However,
the differences are smaller because fewer specialized funds
are used in each simulation, thus reducing the scope for
improvement. We obtain similar results when maximizing
expected returns while holding the variance constant (table
8, bottom panel).21
To capture the idea that mutual funds might have longterm investment horizons, table 9 shows the results with
daily data but with longer holding periods. The portfolio
weights are held constant for different time periods (1, 5,
20, 60, and 120 business days). The results show that the
simulated global funds consistently generate higher returns
than global funds. Interestingly, these excess returns do not
vary significantly across the different holding periods. This
is consistent with the idea that the large gains from diversification come from the simulated funds holding many more
stocks than the actual global funds.22
In sum, the evidence from our simulations suggests that
one can reject the hypothesis that there are no gains from
further international diversification by holding more stocks
within and across countries. Although there is some heterogeneity in the results, the simulated global funds consistently yield higher returns with no greater volatility than the
actual global funds within the same mutual fund families.
The findings also suggest that factors other than transaction costs are important to the behavior of mutual funds.
First, we compare the performance using risk-adjusted
returns. To the extent that specialized funds hold smaller
(less liquid) companies with more volatile returns, this
effect is already captured in our estimations (we find excess
returns after conditioning for volatility). Second, even when
considering non-risk-adjusted returns, holding smaller firms
does not have to affect the ex post mutual fund returns.
Mutual fund returns already embed the potentially higher
transaction costs they incur when trading smaller stocks. So
21
These results are not driven by significant changes in the weights of
the simulated global funds over time. The time series of the portfolio
weights typically change smoothly, and the simulated portfolios do not
require large shifts in holdings, which could entail large transaction costs.
The results above hold when we modify the objective function to account
for the possibility that managers care about their performance relative to a
benchmark index. The results are also similar when we use rolling windows of the last 240 business days instead of using all past information.
See the online appendix and the working paper version of this paper
(Didier et al., 2010) for these results.
22
The possibility also exists that different mutual funds pursue different
stock trading strategies, which might explain the difference in returns
between global and simulated global funds. However, the entropy measures between two consecutive years that capture the similarity of mutual
fund portfolios over time are very stable and not statistically different
across fund types, which suggests that stock turnover is similar across
portfolios. See the online appendix.
12.48%
11.14%
16.67%
12.47%
7.11%
9.74%
17.49%
9.86%
6.28%
6.04%
10.54%
6.80%
5.05%
5.70%
9.78%
6.06%
6.77%
8.23%
13.07%
8.39%
5.05%
5.70%
9.78%
6.06%
10.68%
10.49%
14.21%
11.12%
11.33%
9.70%
15.16%
11.13%
6.28%
6.04%
10.54%
6.80%
6.22%
6.03%
10.53%
6.78%
11.01%
9.95%
15.23%
11.14%
6.22%
6.03%
10.53%
6.78%
Simulated
Global
Funds
3.52%
3.85%
7.20%
4.23%
6.09%
4.98%
5.74%
5.52%
4.46%
4.49%
3.59%
4.34%
2.80%
2.54%
3.27%
2.75%
5.08%
3.74%
4.44%
4.36%
4.85%
4.03%
4.55%
4.42%
Average
Difference
in Returns
4.02%
4.58%
3.92%
4.27%
2.05%
2.25%
1.99%
2.14%
0.87%
0.97%
0.86%
0.92%
4.02%
4.58%
3.92%
4.27%
2.05%
2.25%
1.99%
2.14%
0.87%
0.97%
0.86%
0.92%
Global
Funds
Number of
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Global
Funds
Simulated
Global
Funds
4.18%
4.86%
4.49%
4.54%
2.13%
2.30%
2.10%
2.20%
0.83%
0.92%
0.83%
0.87%
3.89%
4.62%
3.96%
4.24%
1.92%
2.13%
1.90%
2.01%
0.78%
0.89%
0.80%
0.84%
8.07%
5.11%
7.87%
6.65%
6.81%
5.09%
7.67%
6.13%
9.78%
7.33%
11.93%
8.95%
9.50%
7.69%
11.62%
8.97%
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165
63
77
25
165
63
77
25
165
7.78%
5.21%
7.37%
6.51%
8.07%
5.11%
7.87%
6.65%
6.81%
5.09%
7.67%
6.13%
9.97%
7.75%
14.06%
9.54%
10.87%
8.35%
13.55%
10.08%
9.60%
7.98%
11.22%
9.08%
63
7.78%
8.87%
77
5.21%
6.71%
25
7.37%
10.29%
165
6.51%
8.07%
B. Maximizing Expected Returns
63
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2.52%
2.51%
6.46%
3.11%
3.20%
3.20%
5.51%
3.55%
2.86%
2.98%
3.59%
3.02%
1.58%
1.62%
2.90%
1.80%
2.44%
2.33%
4.08%
2.64%
2.79%
2.75%
4.00%
2.95%
Average
Difference
in Returns
5.42%
4.60%
4.43%
4.89%
2.66%
2.25%
2.17%
2.40%
0.91%
0.97%
0.92%
0.94%
5.42%
4.60%
4.43%
4.89%
2.66%
2.25%
2.17%
2.40%
0.91%
0.97%
0.92%
0.94%
Global
Funds
4.52%
4.78%
4.81%
4.68%
2.37%
2.26%
2.22%
2.30%
0.85%
0.92%
0.88%
0.88%
4.28%
4.57%
4.37%
4.43%
2.16%
2.16%
2.03%
2.14%
0.84%
0.90%
0.85%
0.87%
Simulated
Global
Funds
Standard Deviation of Returns
Simulations Using the Longest Available Sample
Average Returns (per Year)
A. Minimizing the Variance of Returns
Simulated
Global
Funds
Standard Deviation of Returns
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Number of
Comparisons
This table shows the differences in the average and the standard deviation of mutual fund returns between the actual and simulated global funds. The results are shown for daily, weekly, and monthly (20 business days) returns. The simulated global funds are constructed from
the actual global and specialized funds within the same mutual fund family by using two different procedures. Panel A shows the results from minimizing the variance of returns subject to a restriction on expected returns. Panel B shows the results from maximizing expected
returns subject to a restriction on the variance of returns. The simulations that use the portfolios with the largest number of specialized funds (the longest time series) for each global fund in each family are reported in the left (right) six columns. The pools of world or foreign funds
are simulations that include several world (foreign) funds within the same family but with different investment natures (e.g., value, growth, or blend funds). The portfolio weights are updated every period. The realized returns of the simulated portfolios are calculated out-ofsample. The annualized differences in returns are calculated over the entire sample for each simulation. The averages across simulations are then computed and reported.
Daily data
World funds
Foreign funds
Pools of world or foreign funds
Total
Weekly data
World funds
Foreign funds
Pools of world or foreign funds
Total
Monthly data
World funds
Foreign funds
Pools of world or foreign funds
Total
Daily data
World funds
Foreign funds
Pools of world or foreign funds
Total
Weekly data
World funds
Foreign funds
Pools of world or foreign funds
Total
Monthly data
World funds
Foreign funds
Pools of world or foreign funds
Total
Type of Global Funds
Global
Funds
Average Returns (per Year)
Simulations Using the Largest Number of Funds
TABLE 8.—GLOBAL FUND SIMULATIONS AT VARIOUS DATA FREQUENCIES
1576
THE REVIEW OF ECONOMICS AND STATISTICS
Holding period: 1 business day
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 5 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 20 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 60 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 1 business day
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 5 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 20 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 60 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Holding period: 120 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
Type of Global Funds
10.85%
10.75%
14.97%
11.42%
11.24%
10.61%
14.92%
11.49%
6.22%
6.03%
10.53%
6.78%
6.22%
6.03%
10.53%
6.78%
11.17%
10.27%
14.89%
11.30%
6.22%
6.03%
10.53%
6.78%
10.62%
10.59%
14.56%
11.19%
11.24%
10.18%
15.07%
11.31%
6.22%
6.03%
10.53%
6.78%
6.22%
6.03%
10.53%
6.78%
11.26%
10.15%
15.16%
11.32%
6.22%
6.03%
10.53%
6.78%
10.68%
10.49%
14.21%
11.12%
11.19%
10.03%
15.22%
11.25%
6.22%
6.03%
10.53%
6.78%
6.22%
6.03%
10.53%
6.78%
11.01%
9.95%
15.23%
11.14%
6.22%
6.03%
10.53%
6.78%
Global
Funds
Simulated
Global
Funds
Average Returns (Per Year)
4.96%
4.60%
4.30%
4.69%
4.59%
4.75%
4.30%
4.62%
4.40%
4.59%
3.90%
4.41%
4.46%
4.49%
3.59%
4.34%
4.97%
4.30%
4.20%
4.54%
5.06%
4.23%
4.38%
4.57%
5.08%
4.21%
4.48%
4.58%
5.03%
4.10%
4.53%
4.52%
4.85%
4.03%
4.55%
4.42%
Average
Difference in
Accumulated
Returns
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
0.87%
0.97%
0.86%
0.92%
Global
Funds
Number of
Comparisons
Global
Funds
Simulated
Global
Funds
0.84%
0.92%
0.84%
0.88%
0.84%
0.91%
0.83%
0.87%
0.83%
0.92%
0.83%
0.87%
0.83%
0.92%
0.83%
0.87%
0.80%
0.90%
0.81%
0.85%
0.79%
0.90%
0.81%
0.84%
0.79%
0.89%
0.80%
0.84%
0.78%
0.89%
0.80%
0.84%
0.78%
0.89%
0.80%
0.84%
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
9.96%
7.99%
11.63%
9.29%
9.89%
7.92%
11.75%
9.25%
9.71%
7.80%
11.64%
9.10%
9.50%
7.69%
11.62%
8.97%
63
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165
63
77
25
165
63
77
25
165
63
77
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165
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
6.80%
5.09%
7.67%
6.13%
9.68%
8.07%
11.91%
9.25%
9.68%
8.15%
11.79%
9.28%
9.60%
8.00%
11.26%
9.10%
9.60%
7.98%
11.22%
9.08%
63
6.80%
9.95%
77
5.09%
8.09%
25
7.67%
11.60%
165
6.13%
9.33%
B. Maximizing Expected Returns
63
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63
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A. Minimizing the Variance of Returns
Simulated
Global
Funds
Standard Deviation of Returns
2.94%
3.06%
4.28%
3.20%
2.95%
3.15%
4.14%
3.22%
2.86%
3.01%
3.61%
3.04%
2.86%
2.98%
3.58%
3.02%
3.18%
3.11%
3.94%
3.26%
3.22%
3.03%
3.98%
3.24%
3.16%
2.96%
4.11%
3.21%
2.98%
2.85%
4.00%
3.08%
2.79%
2.75%
3.99%
2.95%
Average
Difference in
Accumulated
Returns
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
0.91%
0.97%
0.92%
0.94%
Global
Funds
0.85%
0.92%
0.88%
0.89%
0.85%
0.92%
0.88%
0.89%
0.85%
0.92%
0.88%
0.88%
0.85%
0.92%
0.88%
0.88%
0.85%
0.91%
0.86%
0.88%
0.84%
0.91%
0.85%
0.88%
0.84%
0.91%
0.85%
0.87%
0.84%
0.91%
0.85%
0.87%
0.84%
0.90%
0.85%
0.87%
Simulated
Global
Funds
Standard Deviation of Returns
Simulations Using the Longest Available Sample
Average Returns (Per Year)
TABLE 9.—GLOBAL FUND SIMULATIONS WITH VARYING HOLDING PERIODS
Simulations Using the Largest Number of Funds
63
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63
77
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63
77
25
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63
77
25
165
63
77
25
165
63
77
25
165
63
77
25
165
63
77
25
165
63
77
25
165
Number of
Comparisons
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1577
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0.86%
0.93%
0.89%
0.89%
Simulated
Global
Funds
0.91%
0.97%
0.92%
0.94%
Global
Funds
3.02%
2.81%
4.57%
3.16%
9.77%
7.84%
12.22%
9.22%
6.80%
5.09%
7.67%
6.13%
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0.85%
0.93%
0.84%
0.89%
0.87%
0.97%
0.86%
0.92%
4.10%
4.38%
4.62%
4.31%
Global
Funds
6.22%
6.03%
10.53%
6.78%
Type of Global Funds
Holding period: 120 business days
World funds
Foreign funds
Pools of world or foreign funds
Total
B. Maximizing Expected Returns
Global
Funds
Number of
Comparisons
Global
Funds
Simulated
Global
Funds
Standard Deviation of Returns
Average
Difference in
Accumulated
Returns
Simulated
Global
Funds
Average Returns (Per Year)
10.38%
10.40%
15.26%
11.11%
Standard Deviation of Returns
Average
Difference in
Accumulated
Returns
Simulated
Global
Funds
Average Returns (Per Year)
Simulations Using the Longest Available Sample
TABLE 9.—(CONTINUED)
Simulations Using the Largest Number of Funds
This table shows the differences in the average and the standard deviation of mutual fund returns between the actual and simulated global funds at different holding periods. These holding periods change according to the frequency at which the portfolio weights are held constant. The results are shown for the following holding periods: 1, 5, 20, 60, and 120 business days. The simulated global funds are constructed from the actual global and specialized funds within the same mutual fund family by using two different procedures. Panel A shows the
results from minimizing the variance of returns subject to a restriction on expected returns. Panel B shows the results from maximizing expected returns subject to a restriction on the variance of returns. The simulations that use the portfolios with the largest number of specialized
funds (the longest time series) for each global fund in each family are reported in the left (right) six columns. The pools of world or foreign funds are simulations that include several world (foreign) funds within the same family but with different investment natures (e.g., value,
growth, or blend funds). The realized returns of the simulated portfolios are calculated out-of-sample. The annualized differences in returns are calculated over the entire sample for each simulation. The averages across simulations are then computed and reported.
THE REVIEW OF ECONOMICS AND STATISTICS
Number of
Comparisons
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finding positive excess returns in mutual funds is indeed
informative.
B. Insurance Premium in the Global Fund Returns
One potential limitation of this mean-variance analysis is
that it does not capture other effects like the possible existence of an insurance premium in the returns of global
funds. Global funds have a greater ability to shift their holdings across countries and regions, and thus to move away
from troubled countries during turbulent times. Therefore,
investors might be willing to pay for this extra flexibility by
requiring lower risk-adjusted returns from global funds. We
evaluate then whether global funds indeed have a better
ability to minimize their losses relative to specialized
funds.
We first analyze higher moments of the distribution of
the returns. In particular, we compare the skewness and the
kurtosis of the global fund returns to those of the simulated
global fund returns, obtained from the mean-variance exercises. The results that use daily data show that the skewness
and the kurtosis of the returns are similar between the actual
and simulated global funds (table 10). Overall, the evidence
suggests that despite the differences in the excess returns,
higher moments of the distribution of the returns are not
considerably different across the actual and simulated global funds. If anything, the kurtosis is lower for the simulated global funds, which indicates that global funds might
not have robust portfolios (their distribution of returns has
fatter tails).
Given the limited information on portfolio holdings at
high frequencies, we also analyze the incidence of negative
returns during turbulent times, which can shed light on
whether global funds avoid realized risks by moving
away from the turbulence-hit countries or regions. Specifically, we compare the realized returns of both the actual
and simulated global funds conditional on large negative
returns in the MSCI Emerging Market Index (our proxy for
turmoil periods).23 The results show that their performances
are typically not statistically different from each other
(table 11). Therefore, global funds do not seem to avoid
large losses when compared to specialized funds.24 As an
alternative, the table shows the return differentials conditional on the periods in which the simulated global funds
perform poorly. In these situations, global funds yield only
slightly higher weekly returns, although the return differentials are not always statistically different from 0. However,
23
The evidence reported here considers only weekly returns. The
results are similar when we analyze monthly returns.
24
A shift of the simulated global funds toward the actual global funds
and away from specialized funds does not seem to be driving these
results. Portfolio weights on the actual global funds are generally stable in
periods in which the MSCI Emerging Market Index falls significantly.
Moreover, this stability in the portfolio weights also suggests that such a
portfolio shift is not behind the evidence related to the higher moments of
the return distribution.
Kurtosis
10.15
[14.56]
12.47
[19.55]
6.57
[5.64]
10.69
[16.31]
10.15
[14.56]
12.47
[19.55]
6.57
[5.64]
10.69
[16.31]
Skewness
0.63
[0.99]
0.83
[1.21]
0.42
[0.49]
0.69
[1.05]
0.63
[0.99]
0.83
[1.21]
0.42
[0.49]
0.69
[1.05]
0.57
[0.40]
0.86
[0.65]
0.57
[0.55]
0.70
[0.57]
0.70
[0.93]
0.97
[0.87]
0.79
[0.90]
0.84
[0.90]
Skewness
6.12
[4.71]
9.28
[6.55]
7.03
[3.95]
7.74
[5.73]
8.78
[16.21]
11.13
[11.13]
9.85
[11.91]
10.04
[13.37]
Kurtosis
Skewness
A. Minimizing the Variance of Returns
63
0.82
[1.10]
77
0.92
[1.23]
25
0.44
[0.43]
165
0.81
[1.10]
B. Maximizing Expected Returns
63
0.82
[1.10]
77
0.92
[1.23]
25
0.44
[0.43]
165
0.81
[1.10]
Number of
Comparisons
13.70
[16.07]
14.18
[20.34]
6.61
[4.48]
12.85
[17.30]
13.70
[16.07]
14.18
[20.34]
6.61
[4.48]
12.85
[17.30]
Kurtosis
Daily Returns
on Global Funds
0.63
[0.51]
0.87
[0.61]
0.60
[0.50]
0.74
[0.57]
0.82
[0.84]
1.06
[0.90]
0.83
[0.88]
0.94
[0.88]
Skewness
7.98
[7.52]
9.55
[6.09]
7.22
[3.69]
8.60
[6.44]
11.19
[12.48]
13.21
[12.37]
10.07
[11.86]
11.96
[12.33]
Kurtosis
Daily Returns
on Simulated
Global Funds
Simulations Using the Longest Available Sample
165
25
77
63
165
25
77
63
Number of
Comparisons
This table shows the average skewness and kurtosis of the returns of the actual and simulated global funds. The simulated global funds are constructed from the actual global and specialized funds within the same mutual fund family by using two procedures. Panel A shows the
results from minimizing the variance of returns subject to a restriction on expected returns. Panel B shows the results from maximizing expected returns subject to a restriction on the variance of returns. The simulations that use the portfolios with the largest number of specialized
funds (the longest time series) for each global fund in each family are reported in the left (right) five columns. The pools of world or foreign funds are simulations that include several world (foreign) funds within the same family but with different investment natures (e.g., value,
growth, or blend funds). The portfolio weights are updated daily. The realized returns of the simulated portfolios are calculated out of sample. The annualized differences in returns are calculated over the entire sample for each simulation. The averages across simulations are then
computed and reported. The standard deviations of both the skewness and the kurtosis of the distribution of returns are reported in brackets.
Total
Pools of world or foreign funds
Foreign funds
World funds
Total
Pools of world or foreign funds
Foreign funds
World funds
Type of Global Funds
Daily Returns on
Global Funds
Daily Returns
on Simulated
Global Funds
Simulations Using the Largest Number of Funds
TABLE 10.—SKEWNESS AND KURTOSIS: GLOBAL FUND SIMULATIONS
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
1579
0.29%
1.61%
4.65%
3.70%
0.27%
1.59%
4.65%
4.11%
0.30%
1.50%
4.06%
3.65%
0.25%
1.48%
4.35%
3.74%
0.30%
1.50%
4.06%
3.65%
0.37%
1.53%
4.00%
3.42%
0.27%
1.49%
4.35%
3.45%
0.37%
1.53%
4.00%
3.42%
Simulated
Global
Funds (P)
1.39
4.10***
4.38***
1.88*
2.63***
3.27***
4.22***
0.96
2.24**
0.81
2.11**
0.40
3.27***
1.71*
2.24**
0.12
0.52%
2.21%
6.06%
11.71%
0.48%
2.18%
6.36%
12.51%
7,292
14,342
1,297
287
4,878
10,193
950
191
0.47%
2.16%
6.01%
12.04%
0.49%
2.14%
5.69%
11.52%
0.47%
2.21%
6.27%
12.41%
0.47%
2.22%
6.23%
12.47%
7,292
0.49%
0.47%
14,342
2.22%
2.19%
1,297
6.23%
6.37%
287
11.89% 12.74%
B. Maximizing Expected Returns
4,878
10,193
950
191
0.02
3.76***
2.96***
1.01
1.32
4.43***
4.84***
2.14**
2.93***
1.89*
1.69*
2.08**
4.03***
2.08**
2.63***
1.57
9,079
12,854
963
146
6,183
9,265
631
100
9,340
12,529
907
156
6,380
8,946
582
99
Simulated
Global
T-test:
Number of
Funds (P) (P) ¼ (G) Observations
A. Minimizing the Variance of Returns
T-test:
Number of
Global
(P) ¼ (G) Observations Funds (G)
Average Conditional
Returns (per Week)
Conditional on Simulated
Global Fund Returns
0.47%
2.23%
6.46%
13.24%
0.47%
2.23%
6.36%
13.02%
0.47%
2.23%
6.46%
13.24%
0.47%
2.23%
6.36%
13.02%
Global
Funds
(G)
0.40%
2.02%
5.43%
10.84%
0.36%
1.98%
5.22%
10.37%
0.37%
1.99%
5.55%
11.36%
0.34%
1.91%
5.25%
10.84%
8.14***
15.01***
15.29***
6.80***
8.68***
15.00***
13.61***
5.89***
11.94***
17.56***
13.60***
4.89***
11.74***
19.92***
13.83***
4.57***
9,297
12,840
1,140
163
6,371
9,273
784
113
9,297
12,840
1,140
163
6,371
9,273
784
113
Simulated
Global
T-test:
Number of
Funds (P) (P) ¼ (G) Observations
Average Conditional
Returns (per Week)
Conditional on Actual
Global Fund Returns
This table shows the average returns of both the actual and simulated global funds conditional on negative returns on the MSCI Emerging Market Index (left four columns), negative returns on the simulated global fund (middle four columns), and negative returns on the actual
global funds (right four columns). The simulated global funds are constructed from the actual global and specialized funds within the same mutual fund family by using two different procedures. The top panel shows the results from minimizing the variance of returns subject to a
restriction on expected returns. The bottom panel shows the results from maximizing expected returns subject to a restriction on the variance of returns. The realized returns of the simulated portfolios are calculated out-of-sample. The simulations are performed on the daily
returns and the portfolio weights are updated daily, but the aggregate weekly returns are reported. The results for the simulations that use the portfolios with the largest number of specialized funds for each global fund in each family and the longest time series for each global fund
in each family are reported. The t-statistics for the test of the equality of means are shown. The positive t-statistics mean that the returns of the simulated global funds (P) are larger than those of the global funds (G). Significant at the ***1%, **5%, and *10%.
Largest number of funds simulations
Conditional returns between 0% and -1%
Conditional returns between 1% and -5%
Conditional returns between 5% and -10%
Conditional returns less than 10%
Longest available sample simulations
Conditional returns between 0% and -1%
Conditional returns between 1% and -5%
Conditional returns between 5% and -10%
Conditional returns less than 10%
Largest number of funds simulations
Conditional returns between 0% and -1%
Conditional returns between 1% and -5%
Conditional returns between 5% and -10%
Conditional returns less than 10%
Longest available sample simulations
Conditional returns between 0% and -1%
Conditional returns between 1% and -5%
Conditional returns between 5% and -10%
Conditional returns less than 10%
Global
Funds (G)
Average Conditional
Returns (per Week)
Conditional on MSCI Emerging
Market Index Returns
TABLE 11.—AVERAGE CONDITIONAL RETURNS
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THE REVIEW OF ECONOMICS AND STATISTICS
UNEXPLOITED GAINS FROM INTERNATIONAL DIVERSIFICATION
when global funds do not perform well, the simulated global funds perform significantly better.
VI.
Conclusion
Using a novel micro data set of U.S. mutual funds, this
paper studies how institutional investors diversify their
portfolios internationally. This data set allows us to document new stylized facts and shed new light on the existing
explanations for international portfolio diversification. In
particular, we exploit the fact that mutual fund families have
several funds with different international investment scopes.
To the extent that asset returns are not perfectly correlated,
one might expect mutual funds to hold more securities and
to have greater international diversification as their investment scope broadens. Moreover, the existence of different
types of funds within families enables us to shed new light
on which factors might affect international asset allocations
and whether managers exploit the potential gains from international diversification.
We find that global funds have expanded substantially,
thus giving investors more options to diversify risk. However, regardless of their investment scope, mutual funds
tend to invest in a relatively small number of countries and
firms—about 100 stocks. In fact, as their investment possibilities widen, mutual funds invest in fewer stocks and
fewer countries within each region of exposure. This reduction in the number of stocks is not matched by a reduction
in the number of economic sectors in which they invest;
global and specialized funds have a similar sectoral allocation. While the number of stock holdings is comparable
across funds within mutual fund families, there is significant variability in the number of holdings across families.
Several conclusions can be drawn from our analysis.
First, the results that use portfolio holdings suggest that the
restrictive investment practices of mutual funds are not driven by instrument availability or transaction costs, which
are broadly understood to be barriers to purchase securities.
Mutual funds purchase only a very small fraction of the
instruments available for investment. Moreover, specialized
funds invest in assets that are also available to global funds;
this indicates that no clear restrictions exist for global funds
to purchase these securities. Furthermore, neither specialized nor global fund holdings are very large relative to the
firms’ market capitalization. Therefore, this pattern of
investment in a few firms does not seem to be driven by
fund size, because mutual funds might be able to expand
their exposures, probably without incurring major trading
costs.
Second, the evidence in this paper suggests that organizational aspects might help explain the investment choices of
institutional investors. This evidence does not seem consistent with the idea that the asset allocation is driven by the
lack of information at the family level. In particular, we
assess the potential diversification gains from investing in
assets already held within a mutual fund family for which
1581
the company as a whole has already paid the cost of gathering and processing information. In principle, any mutual
fund manager within the company could access the information on these assets. However, the portfolios of the
mutual funds that invest in the same region do not appear to
be very similar when comparing funds within the same
family. Their similarity does increase, though, when the
funds share asset managers. This evidence points to competition between managers.25 Competition might also explain
the stylized fact that a limited number of assets exist in the
mutual fund portfolios, independent of the investment
scope. To the extent that managers within families gather
and process information independently and have a similar
capacity to handle stocks, they will tend to hold a similar
number of securities. Furthermore, there are strong family
effects for the number of stocks held across fund types and
the portfolio loadings on the top ten assets. For example,
the number of portfolio holdings is similar within mutual
fund companies but different across them, even when funds
across families invest in the same regions and have similar
investment scopes. These family effects are much more
important than other fund-specific and family-specific characteristics considered to affect both the ease of gathering
and processing information and portfolio allocations themselves. These family effects suggest that norms at the company level might determine how different funds choose different portfolios and go beyond restrictions and practices at
the fund level.26
Third, the mean-variance analysis suggests the presence
of significant potential gains from further international
diversification. Global funds could gain in risk-adjusted
terms by replicating the portfolios already held by other
funds within the same company. Furthermore, it is not the
case that global funds yield lower returns in exchange for
an insurance premium. Namely, global funds do not appear
to minimize tail risk despite their ability to shift their holdings across countries and regions. In fact, the skewness and
the kurtosis of global funds are similar to those of specialized funds. In the end, we are able to construct a simulated
global fund from the specialized funds within the family
that has a better risk-return profile than the actual global
fund by using nothing but the exact information that is
available at the family level.
Further work is needed to explain the excess returns of
specialized funds. A possible explanation is that by invest25
Although actual competition within families is difficult to quantify,
some papers find evidence consistent with tournaments within families. In
these tournaments, fund managers try to maximize the pool of assets they
manage to increase their compensation, and more generally respond to
the incentives they face. See, for example, Brown et al. (1996), Chevalier
and Ellison (1999), Carpenter (2000), Chen and Pennachi (2009), Pollet
and Wilson (2008), and Csaszar (2012).
26
Family effects, not fully captured by the observables in the estimations, might more broadly reflect investment policies, top management
decisions, internal optimization algorithms, and incentives inherent to the
organizational structure. See, for example, Nanda, Wang, and Zheng
(2004), Gaspar, Massa, and Matos (2006), and Kempf and Ruenzi (2008).
1582
THE REVIEW OF ECONOMICS AND STATISTICS
ing in more and relatively smaller companies, specialized
funds generate a premium. However, the difference in
returns is present beyond the higher volatility that smaller
stocks might entail. Moreover, the difference exists even
when specialized funds do not carry a higher tail risk and in
the strategies that would entail lower trading costs. Furthermore, mutual fund returns are net of any higher transaction
costs they might incur when dealing with smaller companies. So the ex post returns to investors of specialized funds
do not need to exceed those of global funds because the
trading costs are embedded in the fund returns. In sum, even
when transaction costs might be important, the excess
returns of specialized funds seem to depend on other factors.
The evidence presented in this paper points to significant
challenges to the prospects for broad international diversification. To the extent that global funds continue to be large
relative to specialized funds, our findings suggest that the
forgone diversification gains can be significant. At the same
time, many countries and firms might not be able to benefit
from tapping into international investors and might thus
face higher financing costs.
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